The number 9876
9876 is a composite number with 12 divisors. Its prime factorisation is × 3 × 823. Divisors (12): 1, 2, 3, 4, 6, 12, 823, 1646, 2469, 3292, 4938, 9876.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9876: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9876 is composite. Its prime factorisation is
- 3
The divisors add up to 23072; without 9876 itself that is 13196, so 9876 is abundant (13196 is more than 9876). Euler's totient φ(9876) = 3288 numbers up to 9876 share no factor with it.
- 4
The digits of 9876 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9876 = 2^{2} \times 3 \times 823 \]9876 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 23072 |
| Euler totient φ(n) | 3288 |
| Square | 97535376 |
| Cube | 963259373376 |
| Square root | 99.378066 (= 2√2469) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.876 × |
9876 in other forms
| Form | Value |
|---|---|
| In words | nine thousand eight hundred and seventy-six |
| Binary (base 2) | 10011010010100 |
| Octal (base 8) | 23224 |
| Hexadecimal (base 16) | 2694 |
| Base 3 | 111112210 |
| As time | 9876 seconds = 2 h 44 min 36 s |
Is 9876 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9876 ÷ 2 = 4938) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9876 ÷ 3 = 3292) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9876 ÷ 4 = 2469) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9876 ÷ 6 = 1646) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9876 ÷ 12 = 823) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9876 a prime number?
No. 9876 = × 3 × 823, so it is divisible by 2.
What are the factors of 9876?
1, 2, 3, 4, 6, 12, 823, 1646, 2469, 3292, 4938, 9876.
What is 9876 in binary?
10011010010100 (hexadecimal 2694, octal 23224).
What is the square root of 9876?
About 99.3781, exactly 2√2469.
Is 9876 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 9876?
9876 is a happy number: repeatedly adding the squares of its digits reaches 1.